Quasi-periodic Orbits in Siegel Disks/Balls and the Babylonian Problem

0Citations
Citations of this article
2Readers
Mendeley users who have this article in their library.
Get full text
This PDF is freely available from an open access repository. It may not have been peer-reviewed.

Abstract

We investigate numerically complex dynamical systems where a fixed point is surrounded by a disk or ball of quasi-periodic orbits, where there is a change of variables (or conjugacy) that converts the system into a linear map. We compute this “linearization” (or conjugacy) from knowledge of a single quasi-periodic trajectory. In our computations of rotation rates of the almost periodic orbits and Fourier coefficients of the conjugacy, we only use knowledge of a trajectory, and we do not assume knowledge of the explicit form of a dynamical system. This problem is called the Babylonian problem: determining the characteristics of a quasi-periodic set from a trajectory. Our computation of rotation rates and Fourier coefficients depends on the very high speed of our computational method “the weighted Birkhoff average”.

Cite

CITATION STYLE

APA

Saiki, Y., & Yorke, J. A. (2018). Quasi-periodic Orbits in Siegel Disks/Balls and the Babylonian Problem. Regular and Chaotic Dynamics, 23(6), 735–750. https://doi.org/10.1134/S1560354718060084

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free